In this paper, we propose the filter graph distance, a dissimilarity measure based on optimal transport, which compares two graphs through the probability distribution of data generated with graph filters.
Graph filters have been largely studied in the field of Graph Signal Processing [1]}, [2]}, and offer a high level of flexibility in modelling the relationship between data and the underlying graph.The data living on a graph is also referred to as a graph signal. Hence, their use in defining filter graph distance permits to capture a wide range of structural graph properties, including local characteristics, global structure, and any combination of spectral graph properties.
